On Friday, February 23, 2018 at 7:06:47 AM UTC-6, Bruno Marchal wrote:
> On 23 Feb 2018, at 12:40, Lawrence Crowell <goldenfield...@gmail.com 
> <javascript:>> wrote:
> On Thursday, February 22, 2018 at 6:38:15 AM UTC-6, Bruno Marchal wrote:
>> > On 21 Feb 2018, at 20:40, Brent Meeker <meek...@verizon.net> wrote: 
>> > 
>> > 
>> > 
>> > On 2/21/2018 1:32 AM, Bruno Marchal wrote: 
>> >> I guess you mean enumerable here. I don’t see what physical bounds 
>> have to do with Church-Turing thesis, though. We laws suppose that the 
>> universal machine have potentially unbounded time and space (in the non 
>> physical computer science sense) available for them. 
>> > 
>> > But they are bounded in the physical sense, and not just potentially. 
>> But Church-Turing thesis has nothing to do with physics or the physical 
>> sense. 
>> Then you don’t know if a machine, even in the physical world is bounded, 
>> unless you make special assumption on some existing universe. 
>> With mechanism, there are no evidence for a physical primary universe. We 
>> would have found one if we would have discover a serious discrepancy 
>> between the Nature’s physics and the physics in the “head of the number”, 
>> but we have tested this as far as possible, and found none. 
> The relationship between the physical world and mathematics of computation 
> is something I explore here 
> <https://physics.stackexchange.com/questions/305346/is-there-something-similar-to-g%C3%B6dels-incompleteness-theorems-in-physics/305368#305368>.
> This is in connection with the theoretical concept of hypercomputation. 
> Certain types of spacetimes called MH (Malament-Hogarth spacetimes) have 
> the physical properties that might do an end run around the limits of 
> Godel. On the other hand quantum mechanics might provide limits on that.
> I know the existence of MH spacetimes, but it is not yet clear how this 
> escapes Gödel incompleteness. Since Turing we know that hyper-computations 
> do not escape incompleteness. It escapes PA and ZF, but it does not lead to 
> effective way to emulate something not Turing emulable, but I would need 
> more time to assess this, and I judge from an early draft I saw on this 
> subject.
> Then you say in your blog “Physics, on the other hand, ultimately attempts 
> to model reality.” But that is the main axiom of Aristotle metaphysics 
> which is doubted at the start when we realise that all computations are run 
> in arithmetic. You invoke “god” in theology, which means that you don’t 
> intent to do metaphysics or theology with the scientific method. When we do 
> theology or metaphysics with the scientific method we must stay neutral on 
> what could be the fundamental reality, especially when some work like mine 
> give a precise tool to assess if the materiality is fundamental or 
> emerging, and the results get so far abounds in the idea that the material 
> reality is not the fundamental reality. The axioms you are using is refuted 
> by the mechanist hypothesis, so you must take into account that you are 
> postulating a “god” incompatible with Mechanism, but then the MH space-time 
> is out of use in metaphysics, as it requires a black hole to work, and 
> there is few evidence that we have a black hole in our head. 
> Note that I do find the MH-space time very interesting, and it suggest we 
> might exploit computationally back holes in some far future, (or not, as 
> you are right that quantum mechanics makes this theoretically close to 
> impossible), but even if done, it would not change the logical conclusion 
> of Mechanism: physics is just not the fundamental science and physics is 
> constructively reducible to machine’s self-reference theory. You have only 
> the arithmetical reality, which emulates (in the sense of Church, Turing) 
> all computations, and physics is given by the non computable statistics on 
> all relative computational consistent extensions. Although it is not 
> computable, the propositional part of physics is computable and decidable, 
> and indeed we have recovered some quantum logics at the place they were 
> mandatory. This is not just an evidence for computationalism it is also a 
> very deep theoretical evidences for quantum mechanics being completely 
> valid.
> Bruno

The MH spacetime in the case of the Kerr metric does permit an observer in 
principle to witness an infinite stream of bits or qubits up to the inner 
horizon r_- that is continuous with I^+ in the exterior spacetime. This 
means due to spacetime effects one could witness the diagonalization in a 
Zeno machine context. For instance a switch that is switched one in one 
second, off the next half second, on in the next quarter second and so 
forth will presumably have a final state. However, what does prevent this 
in a fundamental way is that a switch flipped in this chirped frequency 
will diverge in energy and become a black hole before returning a result. 
We could of course avoid the black hole with a ball that bounces, but of 
course one does not get an infinite number of little bounces at the end. 
Because of this an observer could in principle witness a universal Turing 
machine emulate all possible Turing machines. Thinking according to TMs is 
for me a bit simpler, but this does illustrate one could get around Godel.

However, quantum mechanics as I illustrate seems to throw a spanner in the 
works. This breaks the continuity between r_- and I_+. It also means the 
inner horizon is built from quantum fields from the exterior in ways that 
generates a mass inflation singularity. This is interesting to ponder with 
respect to the connection between quantum mechanics and general relativity. 
In fact I think the two are simply aspects of the same thing. This means in 
some way the incompleteness theorems of Godel are involved with the 
foundations of physics.


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